cos(x/2)cos(x/4)...cos(x/2^n)
=cos(x/2)cos(x/4)...cos(x/2^n)sin(x/2^n)/sin(x/2^n)
=1/2*cos(x/2)...cos(x/2^(n-1))sin(x/2^(n-1)/sin(x/2^n)
...
=sinx/(2^n*sin(x/2^n))
所以原式=lim(x→0)lim(n→∞)sinx/(2^n*sin(x/2^n))
=lim(x→0)lim(n→∞)sinx/(2^n/x*sin(x/2^n)*x)
=lim(x→0)lim(h→0)sinx/(sinh/h*x) (h=x/2^n)
=lim(x→0)sinx/x
=1
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